Selmer Groups in Twist Families of Elliptic Curves

The aim of this article is to give some numerical data related to the order of the Selmer groups in twist families of elliptic curves. To do this we assume the Birch and Swinnerton-Dyer conjecture is true and we use a celebrated theorem of Waldspurger to get a fast algorithm to compute $$. Having an extensive amount of data we compare the distribution of the order of the Selmer groups by functions of type $\alpha \frac{(\log \log (X))^{1+\varepsilon}}{\log (X)}$ with $\varepsilon$ small. We discuss how the "best choice" of $\alpha$ is depending on the conductor of the chosen elliptic curves and the congruence classes of twist factors.Comment: to appear in Quaestiones Mathematicae. 16 page

Air-snow transfer of nitrate on the East Antarctic plateau – Part 2: An isotopic model for the interpretation of deep ice-core records

Unraveling the modern budget of reactive nitrogen on the Antarctic plateau is critical for the interpretation of ice core records of nitrate. This requires accounting for nitrate recycling processes occurring in near surface snow and the overlying atmospheric boundary layer. Not only concentration measurements, but also isotopic ratios of nitrogen and oxygen in nitrate, provide constraints on the processes at play. However, due to the large number of intertwined chemical and physical phenomena involved, numerical modelling is required to test hypotheses in a~quantitative manner. Here we introduce the model "TRansfer of Atmospheric Nitrate Stable Isotopes To the Snow" (TRANSITS), a~novel conceptual, multi-layer and one-dimensional model representing the impact of processes operating on nitrate at the air–snow interface on the East Antarctic plateau, in terms of concentrations (mass fraction) and the nitrogen (δ15N) and oxygen isotopic composition (17O}-excess, Δ17O) in nitrate. At the air–snow interface at Dome C (DC, 75°06' S, 123°19' E), the model reproduces well the values of δ15N in atmospheric and surface snow (skin layer) nitrate as well as in the δ15N profile in DC snow including the observed extraordinary high positive values (around +300 ‰) below 20 \unit{cm}. The model also captures the observed variability in nitrate mass fraction in the snow. While oxygen data are qualitatively reproduced at the air–snow interface at DC and in East Antarctica, the simulated Δ17O values underestimate the observed Δ17O values by a~few~‰. This is explained by the simplifications made in the description of the atmospheric cycling and oxidation of NO2. The model reproduces well the sensitivity of δ15N, Δ17O and the apparent fractionation constants (15ϵapp, 17Eapp) to the snow accumulation rate. Building on this development, we propose a~framework for the interpretation of nitrate records measured from ice cores. Measurement of nitrate mass fractions and δ15N in the nitrate archived in an ice core, may be used to derive information about past variations in the total ozone column and/or the primary inputs of nitrate above Antarctica as well as in nitrate trapping efficiency (defined as the ratio between the archived nitrate flux and the primary nitrate input flux). The Δ17O of nitrate could then be corrected from the impact of cage recombination effects associated with the photolysis of nitrate in snow. Past changes in the relative contributions of the Δ17O in the primary inputs of nitrate and the Δ17O in the locally cycled NO2 could then be determined. Therefore, information about the past variations in the local and long range processes operating on reactive nitrogen species could be obtained from ice cores collected in low accumulation regions such as the Antarctic plateau

Random Resistor-Diode Networks and the Crossover from Isotropic to Directed Percolation

By employing the methods of renormalized field theory we show that the percolation behavior of random resistor-diode networks near the multicritical line belongs to the universality class of isotropic percolation. We construct a mesoscopic model from the general epidemic process by including a relevant isotropy-breaking perturbation. We present a two-loop calculation of the crossover exponent $\phi$. Upon blending the $\epsilon$-expansion result with the exact value $\phi =1$ for one dimension by a rational approximation, we obtain for two dimensions $\phi = 1.29\pm 0.05$. This value is in agreement with the recent simulations of a two-dimensional random diode network by Inui, Kakuno, Tretyakov, Komatsu, and Kameoka, who found an order parameter exponent $\beta$ different from those of isotropic and directed percolation. Furthermore, we reconsider the theory of the full crossover from isotropic to directed percolation by Frey, T\"{a}uber, and Schwabl and clear up some minor shortcomings.Comment: 24 pages, 2 figure

The Fall of Stringy de Sitter

Kachru, Kallosh, Linde, & Trivedi recently constructed a four-dimensional de Sitter compactification of IIB string theory, which they showed to be metastable in agreement with general arguments about de Sitter spacetimes in quantum gravity. In this paper, we describe how discrete flux choices lead to a closely-spaced set of vacua and explore various decay channels. We find that in many situations NS5-brane meditated decays which exchange NSNS 3-form flux for D3-branes are comparatively very fast.Comment: 35 pp (11 pp appendices), 5 figures, v3. fixed minor typo

Evidence for a novel Carbohydrate Binding Module (CBM) of Tannerella forsythia NanH sialidase, key to interactions at the host-pathogen interface

Bacterial sialidases cleave terminal sialic acid from a variety of host glycoproteins, and contribute to survival and growth of many human-dwelling bacterial species, including various pathogens.Tannerella forsythia, an oral, Gram-negative, fastidious anaerobe, is a key organism in periodontal disease, and possesses a dedicated sialic acid utilisation and scavenging (nan) operon, including NanH sialidase. Here, we describe biochemical characterisation of recombinant NanH, including its action on host-relevant sialoglycans such as sialyl Lewis A and sialyl Lewis X (SLeA/X), and on human cell-attached sialic acids directly, uncovering that it is a highly active broad specificity sialidase. Furthermore, theN-terminal domain of NanH was hypothesised and proven to be capable of binding to a range of sialoglycans and non-sialylated derivatives withKdin the micromolar range, as determined by steady-state tryptophan fluorescence spectroscopy, but it has no catalytic activity in isolation from the active site. We consider this domain to represent the founding member of a novel subfamily of Carbohydrate Binding Module (CBM), involved in glycosidase-ligand binding. In addition, we created a catalytically inactive version of the NanH enzyme (FRIP→YMAP) that retained its ability to bind sialic acid-containing ligands and revealed for the first time that binding activity of a CBM is enhanced by association with the catalytic domain. Finally, we investigated the importance of Lewis-type sialoglycans onT. forsythia-host interactions, showing that nanomolar amounts of SLeA/Xwere capable of reducing invasion of oral epithelial cells byT. forsythiasuggesting that these are key ligands for bacterial-cellular interactions during periodontal disease

Interface Scaling in the Contact Process

Scaling properties of an interface representation of the critical contact process are studied in dimensions 1 - 3. Simulations confirm the scaling relation beta_W = 1 - theta between the interface-width growth exponent beta_W and the exponent theta governing the decay of the order parameter. A scaling property of the height distribution, which serves as the basis for this relation, is also verified. The height-height correlation function shows clear signs of anomalous scaling, in accord with Lopez' analysis [Phys. Rev. Lett. 83, 4594 (1999)], but no evidence of multiscaling.Comment: 10 pages, 9 figure

de Sitter String Vacua from Supersymmetric D-terms

We propose a new mechanism for obtaining de Sitter vacua in type IIB string theory compactified on (orientifolded) Calabi-Yau manifolds similar to those recently studied by Kachru, Kallosh, Linde and Trivedi (KKLT). dS vacuum appears in KKLT model after uplifting an AdS vacuum by adding an anti-D3-brane, which explicitly breaks supersymmetry. We accomplish the same goal by adding fluxes of gauge fields within the D7-branes, which induce a D-term potential in the effective 4D action. In this way we obtain dS space as a spontaneously broken vacuum from a purely supersymmetric 4D action. We argue that our approach can be directly extended to heterotic string vacua, with the dilaton potential obtained from a combination of gaugino condensation and the D-terms generated by anomalous U(1) gauge groups.Comment: 17 pages, 1 figur

Field Theory Approaches to Nonequilibrium Dynamics

It is explained how field-theoretic methods and the dynamic renormalisation group (RG) can be applied to study the universal scaling properties of systems that either undergo a continuous phase transition or display generic scale invariance, both near and far from thermal equilibrium. Part 1 introduces the response functional field theory representation of (nonlinear) Langevin equations. The RG is employed to compute the scaling exponents for several universality classes governing the critical dynamics near second-order phase transitions in equilibrium. The effects of reversible mode-coupling terms, quenching from random initial conditions to the critical point, and violating the detailed balance constraints are briefly discussed. It is shown how the same formalism can be applied to nonequilibrium systems such as driven diffusive lattice gases. Part 2 describes how the master equation for stochastic particle reaction processes can be mapped onto a field theory action. The RG is then used to analyse simple diffusion-limited annihilation reactions as well as generic continuous transitions from active to inactive, absorbing states, which are characterised by the power laws of (critical) directed percolation. Certain other important universality classes are mentioned, and some open issues are listed.Comment: 54 pages, 9 figures, Lecture Notes for Luxembourg Summer School "Ageing and the Glass Transition", submitted to Springer Lecture Notes in Physics (www.springeronline/com/series/5304/

Measurement of the Charged Multiplicities in b, c and Light Quark Events from Z0 Decays

Average charged multiplicities have been measured separately in $b$, $c$ and light quark ($u,d,s$) events from $Z^0$ decays measured in the SLD experiment. Impact parameters of charged tracks were used to select enriched samples of $b$ and light quark events, and reconstructed charmed mesons were used to select $c$ quark events. We measured the charged multiplicities: $\bar{n}_{uds} = 20.21 \pm 0.10 (\rm{stat.})\pm 0.22(\rm{syst.})$, $\bar{n}_{c} = 21.28 \pm 0.46(\rm{stat.}) ^{+0.41}_{-0.36}(\rm{syst.})$ $\bar{n}_{b} = 23.14 \pm 0.10(\rm{stat.}) ^{+0.38}_{-0.37}(\rm{syst.})$, from which we derived the differences between the total average charged multiplicities of $c$ or $b$ quark events and light quark events: $\Delta \bar{n}_c = 1.07 \pm 0.47(\rm{stat.})^{+0.36}_{-0.30}(\rm{syst.})$ and $\Delta \bar{n}_b = 2.93 \pm 0.14(\rm{stat.})^{+0.30}_{-0.29}(\rm{syst.})$. We compared these measurements with those at lower center-of-mass energies and with perturbative QCD predictions. These combined results are in agreement with the QCD expectations and disfavor the hypothesis of flavor-independent fragmentation.Comment: 19 pages LaTex, 4 EPS figures, to appear in Physics Letters